SPOSV - compute the solution to a real system of linear
equations A * X = B,
SYNOPSIS
SUBROUTINE SPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
CHARACTER UPLO
INTEGER INFO, LDA, LDB, N, NRHS
REAL A( LDA, * ), B( LDB, * )
PURPOSE
SPOSV computes the solution to a real system of linear
equations A * X = B, where A is an N-by-N symmetric posi
tive definite matrix and X and B are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**T* U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower
triangular matrix. The factored form of A is then used to
solve the system of equations A * X = B.
ARGUMENTS
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The number of linear equations, i.e., the order of
the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number
of columns of the matrix B. NRHS >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U',
the leading N-by-N upper triangular part of A con
tains the upper triangular part of the matrix A,
and the strictly lower triangular part of A is not
referenced. If UPLO = 'L', the leading N-by-N
lower triangular part of A contains the lower tri
angular part of the matrix A, and the strictly
upper triangular part of A is not referenced.
On exit, if INFO = 0, the factor U or L from the
Cholesky factorization A = U**T*U or A = L*L**T.
LDA (input) INTEGER
The leading dimension of the array A. LDA >=
B (input/output) REAL array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution
matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >=
max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal value
> 0: if INFO = i, the leading minor of order i of
A is not positive definite, so the factorization
could not be completed, and the solution has not
been computed.
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